Since this cash flow will remain the same forever the

Since this cash flow will remain the same forever, the present value of cash flows available to
the firm’s equity holders is a perpetuity. We can discount at the levered cost of equity, so, the
value of the company’s equity is:
PV(Flow-to-equity) = $194,220/.19
PV(Flow-to-equity) = $1,022,210.53
b. The value of a firm is equal to the sum of the market values of its debt and equity, or:
V
L
= B + S
We calculated the value of the company’s equity in part a , so now we need to calculate the
value of debt. The company has a debt-to-equity ratio of .40, which can be written algebraically
as:
B / S = .40
We can substitute the value of equity and solve for the value of debt, doing so, we find:
B /$1,022,210.53 = .40
B = $408,884.21
So, the value of the company is:
V = $1,022,210.53 + 408,884.21
V = $1,431,094.74
4. a. In order to determine the cost of the firm’s debt, we need to find the yield to maturity on its
current bonds. With semiannual coupon payments, the yield to maturity of the company’s bonds
is:
$1,080 = $32.50(PVIFA
R% ,30
) + $1,000(PVIF
R% ,30
)
R = .028497, or 2.8497%
401

402 – SOLUTIONS MANUAL
Since the coupon payments are semiannual, the YTM on the bonds is:
YTM = 2.8497% × 2
YTM = 5.70%
b. We can use the Capital Asset Pricing Model to find the return on unlevered equity. According to
the Capital Asset Pricing Model:
R
0
= R
F
+ β
Unlevered
( R
M
– R
F
)
R
0
= .035 + .95(.11 – .035)
R
0
= .1063, or 10.63%
Now we can find the cost of levered equity. According to Modigliani-Miller Proposition II with
corporate taxes:
R
S
= R
0
+ ( B / S )( R
0
– R
B
)(1 – T
C
)
R
S
= .1063 + (.40)(.1063 – .0570)(1 – .21)
R
S
= .1218, or 12.18%
c. In a world with corporate taxes, a firm’s weighted average cost of capital is equal to:
R
WACC
= [ B /( B + S )](1 – T
C
) R
B
+ [ S /( B + S )] R
S
The problem does not provide either the debt-value ratio or equity-value ratio. However, the
firm’s debt-equity ratio is:
B / S = .40
Solving for B :
B = .4 S
Substituting this in the debt-value ratio, we get:
B / V = .4 S /(.4 S + S )
B / V = .4/1.4
B / V = .29
And the equity-value ratio is one minus the debt-value ratio, or:
S / V = 1 – .29
S / V = .71
So, the WACC for the company is:
R
WACC
= .29(1 – .21)(.0570) + .71(.1218)
R
WACC
= .0999, or 9.99%

CHAPTER 18 -
5. a. The equity beta of a firm financed entirely by equity is equal to its unlevered beta. Since each
firm has an unlevered beta of 1.05, we can find the equity beta for each. Doing so, we find:
North Pole
β
Equity
= [1 + (1 – T
C
)( B / S )]β
Unlevered
β
Equity
= [1 + (1 – .21)($2,400,000/$4,100,000](1.05)
β
Equity
= 1.54
South Pole
β
Equity
= [1 + (1 – T
C
)( B / S )]β
Unlevered
β
Equity
= [1 + (1 – .21)($4,100,000/$2,400,000](1.05)
β
Equity
= 2.47
b. We can use the Capital Asset Pricing Model to find the required return on each firm’s equity.
Doing so, we find:
North Pole:
R
S
= R
F
+ β
Equity
( R
M
– R
F
)
R
S
= .0320 + 1.54(.1090 – .0320)
R
S
= .1502, or 15.02%
South Pole:
R
S
= R
F
+ β
Equity
( R
M
– R
F
)
R
S
= .0320 + 2.47(.1090 – .0320)
R
S
= .2220, or 22.20%
6. a. If flotation costs are not taken into account, the net present value of a loan equals:
NPV
Loan
= Gross Proceeds – Aftertax present value of interest and principal payments
NPV
Loan
= $4,600,000 – .063($4,600,000)(1 – .21)PVIFA
6.3%,10
– $4,600,000/1.063 10
NPV
Loan
= $441,621.98
b. The flotation costs of the loan will be:
Flotation costs = $4,600,000(.025)
Flotation costs = $115,000
So, the annual flotation expense will be:
Annual flotation expense = $115,000/10
Annual flotation expense = $11,500
403

404 – SOLUTIONS MANUAL
If flotation costs are taken into account, the net present value of a loan equals:
NPV
Loan